Advertisements
Advertisements
प्रश्न
Find the middle term of the AP. 95, 86, 77, ........, – 247.
Advertisements
उत्तर
Given A.P. is 95, 86, 77, ....., – 247
Here, a = 95, d = 86 – 95 = – 9
Let the A.P. has n terms.
Then, an = a + (n – 1)d
⇒ – 247 = 95 + (n – 1) (– 9)
⇒ – 247 = 95 – 9n + 9
⇒ – 247 = 104 – 9n
⇒ 9n = 104 + 247
⇒ 9n = 351
⇒ n = 39
Thus, the given A.P. has 39 terms.
Now, Middle term = `[1/2 (39 + 1)]^(th)` term
= `[1/2 (40)]^(th)` term
= 20th term
a20 = a + 19d
= 95 + 19 (– 9)
= 95 – 171
= – 76
As a result, the specified A.P.'s middle term is – 76.
APPEARS IN
संबंधित प्रश्न
Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15th term of that A.P.
The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
In an AP, given a = 7, a13 = 35, find d and S13.
If the sum of first m terms of an A.P. is the same as the sum of its first n terms, show that the sum of its first (m + n) terms is zero
Find the sum of all integers between 84 and 719, which are multiples of 5.
Find the sum of all 3-digit natural numbers, which are multiples of 11.
Show that `(a-b)^2 , (a^2 + b^2 ) and ( a^2+ b^2) ` are in AP.
Find the sum of the following Aps:
i) 2, 7, 12, 17, ……. to 19 terms .
If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)
If the common differences of an A.P. is 3, then a20 − a15 is
The first and the last terms of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?
What is the sum of first 10 terms of the A. P. 15,10,5,........?
The sum of the first n terms of an A.P. is 3n2 + 6n. Find the nth term of this A.P.
The sum of first n terms of an A.P is 5n2 + 3n. If its mth terms is 168, find the value of m. Also, find the 20th term of this A.P.
Let there be an A.P. with first term 'a', common difference 'd'. If an denotes in nth term and Sn the sum of first n terms, find.
Q.18
Find the sum of first 10 terms of the A.P.
4 + 6 + 8 + .............
Find second and third terms of an A.P. whose first term is – 2 and the common difference is – 2.
The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.
Rohan repays his total loan of ₹ 1,18,000 by paying every month starting with the first installment of ₹ 1,000. If he increases the installment by ₹ 100 every month, what amount will be paid by him in the 30th installment? What amount of loan has he paid after 30th installment?
